{
  "id": "2303.09468",
  "version": "v1",
  "published": "2023-03-16T16:39:00.000Z",
  "updated": "2023-03-16T16:39:00.000Z",
  "title": "On the Existence of a Complexity in Fixed Budget Bandit Identification",
  "authors": [
    "Rémy Degenne"
  ],
  "comment": "23 pages",
  "categories": [
    "stat.ML",
    "cs.LG"
  ],
  "abstract": "In fixed budget bandit identification, an algorithm sequentially observes samples from several distributions up to a given final time. It then answers a query about the set of distributions. A good algorithm will have a small probability of error. While that probability decreases exponentially with the final time, the best attainable rate is not known precisely for most identification tasks. We show that if a fixed budget task admits a complexity, defined as a lower bound on the probability of error which is attained by a single algorithm on all bandit problems, then that complexity is determined by the best non-adaptive sampling procedure for that problem. We show that there is no such complexity for several fixed budget identification tasks including Bernoulli best arm identification with two arms: there is no single algorithm that attains everywhere the best possible rate.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-16T16:39:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fixed budget bandit identification",
      "complexity",
      "final time",
      "single algorithm",
      "bernoulli best arm identification"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}